Computation with competing patterns in Life-like automaton

TL;DR

This paper explores a Life-like cellular automaton rule B2/S2345 that exhibits chaotic behavior but can also form localized patterns, enabling the construction of logical gates and arithmetic circuits through pattern interactions.

Contribution

It introduces a novel cellular automaton rule that models chemical media and demonstrates how logical operations can be implemented via pattern interactions.

Findings

Chaotic behavior with localized patterns observed in B2/S2345 automaton.

Logical gates and binary adders constructed using propagating and stationary patterns.

Boolean variables encoded as symmetric and asymmetric patterns competing for space.

Abstract

We study a Life-like cellular automaton rule $B2/S2345$ where a cell in state `0' takes state `1' if it has exactly two neighbors in state `1' and the cell remains in the state `1' if it has between two and five neighbors in state `1.' This automaton is a discrete analog spatially extended chemical media, combining both properties of sub-excitable and precipitating chemical media. When started from random initial configuration B2/S2345 automaton exhibits chaotic behavior. Configurations with low density of state `1' show emergence of localized propagating patterns and stationary localizations. We construct basic logical gates and elementary arithmetical circuits by simulating logical signals with mobile localizations reaction propagating geometrically restricted by stationary non-destructible localizations. Values of Boolean variables are encoded into two types of patterns --- symmetric (False) and asymmetric (True) patterns --- which compete for the `empty' space when propagate in the channels. Implementations of logical gates and binary adders are illustrated explicitly.